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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
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Cap. LXXXI. A E G F B R A.
Wallisii. Vel Sic. Sic quaeris recta CZ. IIDP, et puncta C Nabaxehine inde X
quidistantes, erit 0Z. O F02N = 20ZC =2 v. Hoc est summa peripherix cu-
julvis excerioris et respectirae incerioris est = 2. 2. Numerus harum Summarum est
. Ergo annulus est = 2 x = = ∞8.
Omnis Annuli pars exterior excedit interiorem, duplo rocundi Solidi à Figura
genitrice circa Cuum axem circumacta geniti. Dem. In quavis Z. C. II PMI Cuman-
tur puncta quaeris C N hinc inde ab axe C. MI aequidiltantia, ergo OZ G - 0Z V
=oCN = 2 OCN. Pariter peripheria omnis exterioris exceltus supra correspon-
dentem interiorem est duplus peripheria per punctum exterius de interius cranse.
untis centrumque in axe habentis.
Omnis Annulus Fllipricus (quo nomine comprehendo etiam Circularem) est
ad Sphaerocides FHipleos senicrieis, ur Peripheria media ad Z crasticudinis Annuli.
IJOc CAt _~. PX Z D L:: V. ZDF.
Annulus Parabolicus Clausus est ad genitricis Parabola Conoeides, ut 16 ad 3
Sic enim F. F P Parabola. Ergo Annulus e_ = = F BX E PXOPB. Et Conocicles eIt
=ZF BX Z H. P XOP B. Rrgo AnnuluS. ConOcid:: 3. 8:: 16. 3.
Annutus Parabolicus Patens est ad genitricis Parabolae Conocides, ut r8 semidia-
metri rerolutionis centri graritatis, ad triplam lemilacitudinem. Sit enim D FPF Para-
vola. Ergo Annulus BD =D EXZFIMXOPM. Lt Conocides cA ==Z LIMX = DH.
XOE MI. Ergo Annulus. Conoeid:: ZOPBE. Z OE MI:: T6 PMI. ZEMI.
Annuli Parabolici Clausi pars exterior elt ad interiorem: : FL. 5. nam ParS CX-
cerior = interiori f 2 Conoeid, = inc + (2X38 Annul = 8 Annuli =) 3 ext + 8
InC. ErgOZ ext = s inC. erSO CXF. InL:: FF. 5.
annuli EIliprici pars excerior = inceriori + (2 Sphaerocid =) 223 = x Annul.
EIBOCXE = inC = 4 - = x: exF = inc: hoc est ext - ins. exL F inc: : 4= . vel ext
inC: : 30 -f 4 DF. 3~-- 4DF. Ideoque liquis dac rationem Annuli EIipeici ad
Sphaerocides; vel partis Annuli Elliprici exterioris ad interiorem, dabir Circuli Oua-
draturam.
Sit Figurae genicricis Perimeter s: erit Annuli F. Mipcici superticies =- f .
Annuli Superticies exterior excedit interiorem, dupla superticie Conocideos Pigu-
rae genitricis; oPD =OPF = 2OMF. _C.
Coroll. Annuli Circularis superficies exterior excedic inceriorem, dupla superti-
cie Sphaerae, hoc est octuplo Circuli genitoris.
Annuli Circularis Superticies est ad Circulum genitorem, ut 20 ad radium Cir-
cui genitoris; ideoque ad superticiem Sphaerae, ut a ad diametrum genicoris: )
2Yf:: v. ZY:: 2. ∞. r.
Ponacur P = Superticiei exceriori annuli Circularis. F.180 : r. ~ :: O. P. + 1 =
interiori
2F. = BC. E180~C =, B- +r . ErBOF. I: : rF. rL: : a + 4r C. a
e T. F. 8(.
r I. F 4. 7.C
4r :: v + 4 r. a - 4 r. Proinde E. - T. F. = L: : 8r. 2∞:: 41. v.
Frso quisquis invenit rationem Superticiei annuli Circularis ad Superticiem
Sphaerae; vel ad Criculum genicorem; vel racionem superticiei excerioris ad in.
teriorem: inveniet Circuli Duacraturam.